On which factors, the usage of Ram by an application depend?
Mate, IMO, you need to elaborate your question, as to precisely, what you want to know. I don't think people would like to elaborate the whole OS kernel to make you understand how the application interacts with the OS, the OS kernel and the hardware for the application to work properly.
In short, as far as I know, almost all applications (exe's) have some DLL's (Dynamic Link Libraries) which function as resources to the proper functioning of the application. All the applications need these DLL's to carry on with their specific tasks, take the user input, process it and give the output. Then comes the User Interface (UI) which also takes it's own share of space on the system RAM so that the system can show you what you need want. If the application UI is more graphics intensive (having more use of high quality graphics) it would take more space in the system RAM. Then there are some other OS resources (system DLL's) which let the software application interact with the OS, which in turn interacts with the hardware and gets the work done. So, the higher the number of exe's (applications) that are being run by the application, the dll's and other such resources being used by these exe's the higher would be the use of system RAM.
I hope this would help a bit.